Mathematics education in east africa towards harmonization and enhancement of education quality 1st
Mathematics Education in East Africa Towards Harmonization
and Enhancement of Education Quality 1st Edition Anjum Halai
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Evaluation in Foreign Language Education in the Middle East and North Africa 1st Edition Sahbi Hidri
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Preface
The International Commission on Mathematical Instruction (ICMI) has a substantive interest in ensuring that its resources and influence extend to any country that is able to mobilize the elements of its mathematics education enterprise to make productive use of this connection. In line with this goal, ICMI in conjunction with the International Mathematical Union (IMU), and with the support of UNESCO and ICSU (International Council for Science), promotes the Capacity & Networking Project (CANP). It aims to enhance mathematics education in developing countries by supporting the educational capacity of those responsible for mathematics teachers, and to create sustained regional networks of teachers, mathematics educators and mathematicians, linking them to international support.
CANP consists of a programme in a different developing world region every year: each programme has, at its centre, a two-week workshop of about forty participants, half from the host country and half from regional neighbours, who interact with experts in mathematics, mathematics education, and school policy coming from different parts of the world. It is primarily aimed at mathematics teacher educators, but each event includes also mathematicians, researchers, policy makers, and key teachers.
The Capacity & Networking Project is a major international initiative in the mathematical sciences in the developing world to help exchange information, share state of the art research, enhance mathematics education and build a sustainable network for policy makers, scholars and practitioners across those targeted regions.
The programme builds on existing activities in the region and does not seek to reproduce or compete with existing development programmes.
At the time when this book is printed (2016) five CANP workshops have been held: CANP-1 in Sub Saharan Africa (2012), CANP-2 in Central America and Caribbean Area (2012), CANP-3 in South East Asia (2013), CANP-4 in East Africa (2014), CANP-5 in Andean Region and Paraguay (2016).
The main goal of a CANP consists in building capacity in mathematics education and creating a sustainable regional network in the countries, which participate in the workshop, with a common goal of improving mathematics education in the
region. The initial two-week workshop is an occasion for launching the network and for collecting and sharing information about the situation of mathematics teaching in the region. For this, before the workshop each group of participants from a country prepares a report about the state of the art in their own country: the reports are presented, compared and discussed during the meeting. After that, they are further elaborated according the results of the discussions and constitute a final report for that CANP.
They constitute interesting documents about mathematics education in the regions touched by the different CANPs, and give a piece of information not always accessible in an easy way. For this reason ICMI decided to launch a new series of books with an international publisher, Springer, in order to make accessible non-expensive format reports to an international audience of informed policy makers and scientists.
The present volume is the first in the series of CANP reports: it is the result of a huge work of elaboration of the original documents presented at CANP-4 workshop, held from September 1st to 12th, 2014 at the Aga Khan University Institute for Educational Development East Africa, in Dar es Salaam, Tanzania. The event involved more than 80 participants from Tanzania, Kenya, Uganda and Rwanda; it was organised in a splendid way thanks to the wonderful work both of the International Programme Committee, and of the Local Organising Committee (LOC), and especially of Anjum Halai, chair of the LOC, and her team. The Aga Khan University Institute for Educational Development East Africa supported the event in a number of ways which made it possible to offer such a rich programme. In fact CANP-4 included lectures given by outstanding mathematicians and mathematics educators, regional presentations, workshops, round table discussions, panel presentations, and other parallel activities (school visits, mathematical games, traditional dance, poems). Many hours were devoted to the discussion of the regional reports, which are the germs from which this book was originated, and to the creation of an East Africa Mathematics Education and Research Network, chaired by Alphonse Uworwabayeho from Rwanda who is ably supported by Angelina Bijura from Tanzania.
The editors of the volume, Anjum Halai and Geoff Tennant, and the other authors, Peter Kajoro, Simon Karuku, Mussa Mohamed, Veronica Sarungi, and Alphonse Uworwabayeho, made a huge effort to have the different articles written according to what they call the ‘Harmonization and Enhancement of Education Quality’ issues. They are nicely illustrated in the book: the main idea is to show the necessity in Eastern Africa countries of equipping the students with those mathematical skills that will enable them to compete effectively in the East African Community’s (EAC’s) envisaged common market and to facilitate mobility of students and teachers across the EAC partner states. The six chapters of the book show the related difficulties and possibilities for the school systems in EAC, which come from a different colonial past (British and Belgian).
I thank all those who have made possible the existence of this book: the editors, the authors, the publisher, and particularly the participants to the CANP-4 event. I do think that making its content accessible to mathematics educators, teachers, and
policy makers represents a useful tool for approaching the problems of mathematics education within a global landscape, but without forgetting the specific cultural and social needs of a developing region, in this case the EAC.
It is my strong hope that with the publication of the other CANP books, we will have a wide updated picture of mathematics education needs and problems from relevant parts of the developing world. This will help to avoid the dangers of the alienation generated by the loss of the variety of cultural richness existing in the different regions of the world.
January 26, 2016
Ferdinando Arzarello
President of the International Commission on Mathematical Instruction
Editors and Contributors
About the Editors
Anjum Halai is a professor of education currently working at the Aga Khan University Institute for Educational Development in Tanzania. From teaching mathematics in secondary schools to graduate teaching and supervision, she has substantial experience in the field of mathematics education, especially in technologically less developed countries including Pakistan, Kenya Tanzania and Uganda. Anjum Halai obtained her DPhil from Oxford University in the UK. Her research interests include issues of social justice in classroom settings where learners are marginalized on the basis of language, gender, conflict and other forms of exclusion.
Geoff Tennant is associate professor and head of teaching programmes at the Institute of Educational Development, East Africa, Aga Khan University. He has previously worked in University-based secondary mathematics initial teacher training in the UK. His research interests reflect the concern that all children should have maximal access to the school curriculum, particularly in mathematics, including forming meaningful links between number and introductory algebra.
Contributors
Peter Kajoro is assistant professor at the Aga Khan University Institute for Educational Development, East Africa. He previously taught mathematics and science in schools in Dar es Salaam, Singida and Tabora. He is part of a team writing mathematics textbooks for secondary schools in Tanzania, particularly aimed at supporting students as they make the transition from Swahili to English as the medium of instruction. He is research interests also include teacher education and the use of dynamic geometry software in the mathematics classroom.
Simon Karuku is a lecturer in mathematics education at Embu University College in Kenya. For the past four years, he has taught and researched on mathematics and mathematics education at various institutions, including the Institute for Educational Development, East Africa Aga Khan University. He obtained his PhD in Mathematics Education from the University of Alberta, using a phenomenological approach to analyse the nature of help in the mathematics classroom. His research interests include the dynamics of student–teacher interactions in mathematics teaching and learning.
Mussa Mohamed is a lecturer in science education at the Aga Khan University Institute for Educational Development, East Africa. He has an undergraduate degree in science with education from the University of Dar es Salaam and a Master of Education degree from Aga Khan University. His research interests focus on promoting scientific and mathematical literacy in the early years.
Veronica Sarungi is a lecturer currently working at the Aga Khan University’s Institute for Educational Development, East Africa (IED-EA) in Tanzania. She previously worked as a secondary mathematics teacher and is currently involved in mathematics education, including in-service programs for teachers in Tanzania, Kenya and Uganda. Veronica has a Masters in Education specialising in mathematics and science from IED-EA. Her research interests include mathematics teacher education, specific learning difficulties in mathematics and numeracy for early years’ learners.
Alphonse Uworwabayeho is senior lecturer at the University of Rwanda College of Education. He was previously a mathematics teacher in secondary schools. He is currently leading the university department responsible for Teacher Training Colleges. He gained his PhD on integrating ICT in the teaching and learning of mathematics at the University of Bristol, United Kingdom. His research interests lie in professional development in the Rwandan context via a model of participatory action research that involves mathematics teachers in developing innovative classroom scenarios through hands on experimentation with ICT and reflection and discussion with other teachers.
Introduction
In the increasingly global and technological world, mathematics is seen as a significant gatekeeper of opportunities for social and economic advancement and mobility. Hence, in the context of a post-2015 scenario (2015 was the target year to achieve the Millennium Development Goals led by UNESCO, see unesco.org), countries and development agencies in the East Africa region and more broadly are looking towards increasing access to a relevant and high-quality secondary education as a lever towards economic development (World Bank 2011; UNESCO 2012). Policy makers and other key decision makers in education are looking towards improvement in mathematics teaching and learning as a key focus in education reform. In the East Africa region also, a number of initiatives have been taken at the national levels to improve the quality of mathematics education. For example, these include the SMASSE1 initiative in Kenya, the SESEMAT2 in Uganda and similar initiatives in Tanzania all significantly supporting the quality of mathematics education and/or mathematics teacher education in the respective country. However, relatively little is known about the quality of secondary mathematics education in the East Africa region from the perspective of: (a) mathematics curriculum and syllabus in public secondary schools; (b) teaching and learning in public secondary mathematics classrooms; (c) achievement in mathematics; and (d) mathematics teacher education. Hence, this report aims to present, and discuss critically, the content, process and outcomes of secondary mathematics education in the region, provide a comparative perspective of the issues in mathematics
1“Strengthening Science and Mathematics in Secondary Education” (SMASSE), a significant initiative in science and mathematics education, was launched by the Ministry of Education in collaboration with the Japan International Cooperation Agency in 1998 and further extended. 2Secondary Science Education and Mathematics Teachers (SESEMAT) Project initiated by the Ministry of Education and Sport in collaboration with the Japan International Cooperation Agency since 2004.
education in the four countries and make recommendations for policy and practice. It addresses the following two broad questions:
• What is the state of secondary mathematics education in East Africa?
• Comparatively, what are the possibilities, issues and challenges in improving the state of secondary mathematics education in the region?
This edited collection is expected to be an invaluable source of information and knowledge for academics, practitioners and policy makers to reflect on their own practices as it brings insights mainly from developing countries where relatively less research activity takes place.
The book is expected also to be a valuable resource for courses in mathematics education and related social sciences both at the graduate and undergraduate levels, as well as for students of international development.
This work was undertaken over a nine-month period (November 1, 2013–July 31, 2014) by a team of experienced mathematics education researchers in the region. Methodology involved looking at: (a) key recent or ongoing initiatives and reform projects in secondary mathematics education undertaken by the respective Ministry of Education independently or in collaboration with international development partners; (b) examination achievement results of the national examination councils in the four countries; (c) syllabus and curriculum content and related documents in the public secondary schools in the four countries; (d) teacher education curriculum and syllabus and related documents; and (e) a review of classroombased studies and projects in the four countries.
Every effort was made including two cycles of peer review to ensure quality, comprehensiveness, accuracy and validity of information in the book.
References
UNESCO. (2012). Challenges in basic mathematics education. Paris: UNESCO. ISBN 978-92-3-00-071-3.
World Bank. (2011). A regional exploration of the pathways towards harmonization of math & science curriculum in the East African Community. Ministerial Forum Summary Report.
Chapter 1 Issues for Quality Enhancement and Harmonization of Education in East Africa
Mussa Mohamed, Anjum Halai and Simon Karuku
Abstract This chapter provides a description of the historical and political development of the current mass education system in East Africa. It goes on to provide a comparative analysis of the structure of the school education system in the East African countries, Kenya, Rwanda, Tanzania and Uganda. Finally, on the basis of the historical and comparative analysis of the education system the chapter raises questions for harmonization of the education system in the partner states in the East African Community.
Introduction
The system of formal education as currently found in the East African region has its roots in the colonial history of the region. After independence, the education system was characterized by strong structural continuity but also by significant change. Perhaps owing to their common colonial ancestry, Kenya, Tanzania and Uganda opted for a common education system—the one inherited from the former British administration. On the other hand, Burundi and Rwanda charted their own independent courses of education, closely mirroring the education system of their Belgian colonial masters. In recent years, however, there has been a gradual shift in policy within the East African Community (EAC), informed by the region’s
M. Mohamed (*) · A. Halai
Aga Khan University Institute for Educational Development East Africa, Salaama House Urambo Street, PO125, Dar es Salaam, Tanzania
e-mail: mussa.mohamed@aku.edu
A. Halai
e-mail: anjum.halai@aku.edu
S. Karuku
Embu University College, P.O. Box 6, Embu 60100, Kenya
A. Halai and G. Tennant (eds.), Mathematics Education in East Africa, SpringerBriefs in Education, DOI 10.1007/978-3-319-27258-0_1
socio-economic needs. In particular, there is a concerted effort to harmonize the region’s education system with the aim of attaining an “increasingly networked and interrelated group of curriculum and examination systems, linked in such a way that these systems possess overlapping, interconnected and comparable logics that are capable of influencing each other across the partner states” (East African Community 2012).
Ultimately, the goal is to equip students with skills that will enable them to compete effectively in the EAC’s envisaged common market and to facilitate mobility of students and teachers across the EAC partner states. The catalyst for this harmonization agenda is the ongoing effort to revive the EAC. EAC is a regional intergovernmental organization comprising Burundi, Kenya, Rwanda, Tanzania, and Uganda. It was originally established in 1967, with Kenya, Tanzania and Uganda as its only members, disbanded in 1977, and re-established in 2001.
A key purpose of this chapter is to provide the context and background of the secondary school education system in four of the partner states in the EAC; namely, Kenya, Rwanda, Tanzania, and Uganda.1 The chapter begins with a brief historical account on formal education system in East Africa, with consideration of the economic situation. This is followed by a description of the structure of current school system in the post-independence East Africa, with some closing reflections on implications for harmonization.
Historical Background of Education in East Africa
The earliest system of education in East Africa was oral in nature. Its main objective was to ensure that the next generation inherited the culture, customs and rules of engagement in the society (Merriam 2007). In other words, its main objective was to mould individuals to fit into the society (Omari and Mosha 1987). A lot of emphasis was placed on communal virtues and collective responsibilities. Members of the larger kin network were collectively responsible for the upbringing of children and teaching to them values and norms of their family, society and culture. These values and norms were transmitted through various aspects of culture such as folk tales, songs, myths, legends, proverbs and riddles.
The philosophy of belonging, living together, and bravery was deep rooted in East African informal education. For example, among the Kiswahili speakers, there were proverbs that emphasized communalism; such as mtu ni watu (one can only be defined in the context of others; Mbiti 1970). The indigenous education also encouraged hard work using such proverbs as ‘mtaka cha mvunguni sharti ainame’ (the one who desires that which is underneath must stoop; Moumouni 1968).
1While the issues covered in this volume are largely relevant to all the five partner states in the EAC, the in-depth focus does not cover Burundi.
The formal education system of the kind that is prevalent in East Africa today was established in the colonial period mainly through the Christian missionaries with the aim of directing “the conduct of individuals to respect and worship God” (Lawuo 1975). One of the key policy pronouncements that formalized the education system in East Africa was provided by the Phelps-Stokes Commission of 1919–1924. This commission emphasized that education provided to East African countries be adapted to the East African rural environment and required that all schools be registered, use the government prescribed syllabus, and be supervised by government inspectors (Masudi 1995). One of the shortcomings of the colonial education system was that it did not reflect the needs, interests and values of East Africans. Instead, its main aim was to prepare the ‘natives’ to be used in the administration of the colony, and to inculcate in them a liking for order, cleanliness, diligence, dutifulness, and a sound knowledge of the colonialists’ customs and culture (Omari and Mosha 1987; Brock-Utne 2006). Most of the schools had three streams; namely (a) a stream for the ‘bright pupils’, who were mainly taught the 3Rs; i.e., reading, writing and arithmetic; (b) a stream for less academically able pupils, who were mainly taught industrial skills; and (c) a stream for the ‘dull pupils’, who were mainly taught agricultural labor skills (Gottneid 1976).
At independence (Kenya in 1963, Rwanda in 1962, Tanzania in 1961 and Uganda 1962), the four East African countries inherited an educational system that was mainly racially segregated: there were separate schools for those of European, Asian and African descent (Arunsi 1971; Galabawa 1990; Wasonga 2012). The education system for those of African descent was mostly in the hands of the missionary groups (Arunsi 1971), and had the stated aims of ‘re-socializing’ them, facilitating evangelization, and meeting the colonial administrative objectives (Jimenez and Lockheed 1995; Omari and Mosha 1987). During the first years of independence, the East African countries were under enormous pressure to increase access to education.
A significant influence on education in post-independence East African states was the Addis Ababa Conference of Education for Africa in May 1960 (UNECA/UNESCO 1961). The conference observed the non-contextual nature of education provided by colonialists and came up with recommendations that the African education authorities should revise and reform education in the areas of curricula, textbooks and teaching methods, so as to take account of the African environment, child development, cultural heritage, and the demands of technological progress and economic development (UNECA/UNESCO 1961).
Cultural and Socio-Economic Background of the Countries
Before proceeding to consider the structure of education across the region more fully, the educational scene is put into the context of the cultural and socio-economic situation in which the countries operate.
Table 1.1 Selected socioeconomic indicators of East African countries. Norway and Niger have been included in the table to aid comparison
Source UNDP (2014), World Bank (2014)
aThe Human Development Index (HDI) is a value assigned to a country between 0 and 1, giving a measure for average life expectancy, education and personal income. For more information see http://hdr.undp.org/en/content/human-development-index-hdi
bMean years of schooling: years that a 25-year-old person or older has spent in schools
cExpected years of schooling: years that a 5-year-old child is expected in spend in education over a lifetime
dGross Domestic Product
The East African Community (EAC) region covers an area of 1.8 million square kilometers with a population of about 143.5 million (East African Community 2014). The region reflects diversity of culture, language, ethnic and religious identities. As can be seen in Table 1.1, the four countries are not the poorest in Africa, but in terms of life expectancy, schooling and gross domestic product they fall well below Norway which, according to the Human Development Index, comes at the top of the list.
Educational Structure in the EAC
In terms of the structure of the education system, the East African countries continued with the structure they inherited from their colonial masters. For example, between 1967 and 1977, Kenya, Uganda and Tanzania had a single system of education under the East African Community—consisting of 7 years of primary education, 4 years of ordinary level secondary education (O-level), 2 years of advanced level secondary education (A-level) and at least 3 years of university education; that is, 7-4-2-3+. When the East African Community collapsed in 1977, each of the three countries continued with the same system of education. In 1985, however, Kenya adopted a new education system consisting of 8 years of primary education, 4 years of secondary education and at least 4 years of university education; that is, 8-4-4+. To date, Tanzania and Uganda are still using the post-1977 system of education. The only difference between the two systems of education is in the number of years of pre-primary education—two years
Kenya P123456789101112
Rwanda P123456789101112
Tanzania P12345678910111213
Uganda P12345678910111213
KEY
AdvancedSecondary(A-level)
OrdinarySecondary(O-level)
Secondary
Primary
Pre-primary
Fig. 1.1 The structure of pre-university education in Kenya, Rwanda, Tanzania, and Uganda
in Tanzania and three years in Uganda. As noted above, Rwanda is a member of the new East African Community. Her education system has also evolved since independence, and currently follows a 3-6-3-3-4+ structure; that is, 3 years of preprimary education, 6 years of primary education, 3 years of ordinary secondary education (O-level), 3 years of advanced secondary education (A-level), and at least 4 years of university education.
Figure 1.1 shows the structure of pre-university education in the four countries. Excluding pre-primary education, Kenya and Rwanda have 12 years of preuniversity education, while Tanzania and Uganda have 13 years. In Kenya and Tanzania, the official secondary school-entrance age is 14 years, while in Rwanda and Uganda it is 13 years (East African Community 2012).
In all the four countries, pre-primary (nursery) education is neither free nor compulsory. Pre-schools are either public-, private- or community-owned, and admission into these schools depends on the willingness and ability of the families to meet the school requirements. Primary education, which officially starts at the age of 6 years in Kenya and Uganda and 7 years in Tanzania and Rwanda, is free and compulsory in all the four countries. Whilst the first three years of secondary education are free and compulsory in Rwanda, in the other countries with the exception of Zanzibar2 secondary education is not compulsory, with admission depending on passing the required test (East African Community 2012).
2Zanzibar is semi-autonomous with some aspects of education coming under the control of the Revolutionary Government. In a transition to compulsory secondary education for all, most students who fail the Primary School Leaving Examination are required to repeat the final year of primary school and retake the examination. Those who then fail leave school, whilst all who pass are required to proceed to the first two years of secondary school. After two years of secondary school there is another examination, those who pass are required to stay for two more years, those who fail then leave (see http://www.moez.go.tz/index.php?cq=syst&sys=3 retrieved on 26th February 2015).
Concluding Reflections
The formal educational system in East Africa has gone through several reforms over the years. In contrast to the colonial education system, the post-colonial education system in East Africa is aimed at equipping East Africans with the skills they need to compete nationally, regionally and internationally. Challenges, however, abound in this endeavor, and harmonization of the education systems of the partner states in EAC is seen as an important counterweight to these challenges. With this harmonization, it is envisaged that there will be easy students’ mobility and easy employability throughout the EAC partner states. In recognition of the critical role that mathematics, science and technology play in the development of a country, more priority has been given to the harmonization of the curricula of these subjects (World Bank 2011). The work reported in this volume is expected to offer valuable insights on how best to go about the harmonization process.
References
Arunsi, N. O. (1971). The library and adult education in Tanzania: A survey. In A.-B. Wallenius (Ed.), Libraries in East Africa (pp. 83–124). Uppsala: Scandinavia Institute of African Studies.
Brock-Utne, B. (2006). Whose education for all? The recolonization of the African mind. San Diego, CA: Africana Books.
East African Community (2012). Regional report: Harmonisation of the East African education systems and training curricula. Retrieved January 24, 2015 from http://www.eac.int/ education/index.php?option=com_content&id=73&Itemid=145
East African Community (2014). East African Community facts and figures—2014. Retrieved January 23, 2015 from http://www.eac.int/statistics/index.php?option=com_docman&Itemid=153
Galabawa, C. J. (1990). Implementing educational policies in Tanzania. Washington, D.C.: World Bank.
Gottneid, A. J. (Ed.). (1976). Church and education in Tanzania. Nairobi: East African Publishing.
Jimenez, E., & Lockheed, M. (1995). Public and private secondary education in developing countries: A comparative study. Washington, DC: The World Bank.
Lawuo, Z. (1975). The implementation of British colonial education: Policy in Tanganyika, 1919–1939. Dar es Salaam: University of Dar es Salaam Press.
Masudi, A. (1995). The role of donors and non-governmental organizations in primary education. Papers in Education and Development, 16, 105–116.
Mbiti, J. S. (1970). African religions and philosophy. London: Heinemann. Merriam, E. O. (2007). Learning in adulthood: A comprehensive guide. San Francisco, CA: Jossey-Bass.
Moumouni, A. (1968). Education in Africa. New York: Praeger.
Omari, I. M., & Mosha, H. J. (1987). The quality of primary education in Tanzania. Nairobi: Man Graphics Limited.
UNDP (2014). UN human development report, 2014. Retrieved September 6, 2014 from http://hdr.undp.org/sites/default/files/hdr14-report-en-1.pdf
UNECA/UNESCO (1961). Final report: Conference of African states on the development of education in Africa. Addis Ababa: UNESCO Publishing.
Wasonga, T. A. (2012). Perspectives on K-12 learning and teacher preparation in East Africa. In O. N. Ukpokodu & P. Ukpokodu (Eds.), Contemporary voices from the margin: African educators on African and American education (pp. 129–148). Charlotte, NC: Information Age Publishing.
World Bank. (2011). A regional exploration of pathways towards harmonization of math and science curriculum in the East Africa Community: Discussion paper. Washington, D.C.: World Bank.
World Bank (2014). Countries’ reports. Retrieved September 6, 2014 from http://www.worldbank.org/ en/country.
Chapter 2
Towards a Harmonized Curriculum in East Africa: A Comparative Perspective of the Intended Secondary School
Mathematics Curriculum in Kenya, Rwanda, Tanzania and Uganda
Simon Karuku and Geoff Tennant
Abstract This chapter presents the results and insights gained from a comparative analysis of the national secondary school mathematics syllabuses of Kenya, Rwanda, Tanzania and Uganda. Whilst considerable commonalities were found, it was particularly Rwanda, with a different colonial past, which was found to have a more formal curriculum, exemplified in the lack of mention of measurement below the fourth year of primary school and the absence of approximation as a topic. Differences in sequencing topics were found, e.g. Uganda and Rwanda introduce number sequences in year 4 as a means of contextualizing algebra, Tanzania and Kenya introduce them in year 10 somewhat more formally. The continuance of calculations in shillings and cents in Tanzania and Kenya, and the use of logarithms as a calculation tool in Tanzania, Uganda and Kenya can be taken as evidence of a mismatch between what happens in school and the outside world. Differences are acknowledged between the stated curriculum on the one hand, and what gets taught by teachers and indeed learnt by children on the other. Whilst considerable work has been undertaken already to update the curricula in different ways, further work is required to ensure that the syllabus across the region is fit for purpose for the 21st century, not least in engaging all learners in this important subject.
S. Karuku (*)
Embu University College, P.O. Box 6, Embu 60100, Kenya
e-mail: simon.karuku@embuni.ac.ke
G. Tennant
Aga Khan University Institute for Educational Development East Africa, Salaama House Urambo Street, PO125, Dar es Salaam, Tanzania e-mail: geoff.tennant@aku.edu
A. Halai and G. Tennant (eds.), Mathematics Education in East Africa, SpringerBriefs in Education, DOI 10.1007/978-3-319-27258-0_2
S. Karuku and G. Tennant
Introduction
Mathematics education in the East African region, just like in many parts of the world, faces many challenges and opportunities associated with population growth, technological advancement, regional interdependence, and globalization. In response to these challenges and opportunities, several curricular reforms in mathematics education have been proposed and implemented in the region since independence. The latest of these endeavours is the proposal to have a harmonized curriculum across the partner states in the East African Community (EAC). In a bid to contribute to the ongoing regional debate on how to harmonize the curriculum, a comparative analysis of the national secondary school mathematics syllabuses of four partner states in the EAC—namely, Kenya, Rwanda, Tanzania and Uganda—was carried out. In this chapter, the results of this comparative analysis, as well as the insights drawn from the analysis are discussed. At the end of the chapter is a discussion of the potential implications of the commonalities, differences and gaps identified in the syllabuses for practice, policy, and future research directions. Before proceeding further, however, it needs to be acknowledged that there are, broadly speaking, three ways of considering the curriculum: what is intended by policy makers and the authors of the stated curriculum; what is taught by teachers in classrooms; and what actually gets learnt by students (Cuban 1992). One might reasonably consider that the most crucial aspect of the curriculum is the last, that is, what is actually learnt—Tennant and Sarungi in this volume use achievement scores as a proxy for what actually gets learnt by students. This chapter is concerned with one aspect of the intended curriculum; namely, the content of secondary school national mathematics syllabuses in the four countries. In the following section, we describe the intended aims of mathematics education in the four countries.
Stated Aims and Objectives of Secondary School Mathematics Education
In all the four countries, the mathematics curriculum is developed centrally by an independent governmental agency within the Ministry of Education. In Kenya, the curriculum is designed by the Kenya Institute of Curriculum Development; in Rwanda and Uganda, the agency responsible for curriculum development is known as National Curriculum Development Centre (NCDC), while in Tanzania, it is known as Tanzania Institute of Education (TIE). In each of the four countries the mathematics syllabus specifies what topics must be learnt. It also suggests the teaching, learning and assessment materials that teachers could use in their classrooms.
An analysis of the stated aims and objectives of secondary school mathematics curriculum found that some of the aims are country-specific, while others are more general. For example, one of the general objectives for A-level mathematics
education in Rwanda is to enable the learner to “Use acquired mathematical skills to respect human rights” (NCDC–Rwanda 2010: 5)—a recognition of the potential role that mathematics can play in the realm of citizenship and community building. Some goals are shared by some or all the four countries. For example, there are two general objectives that are common to all the four countries, namely, to enable students to:
(i) think and reason precisely, logically and critically in any given situation, and; (ii) creatively and confidently apply mathematical problem-solving strategies to solve problems in other subject areas and in everyday life.
In addition, there is one general objective that is shared by Kenya, Uganda and Rwanda, namely, to enable students to analyse, interpret and present numerical information meaningfully using tables, graphs, charts, and diagrams. These common objectives could serve as the initial reference points for the harmonization process.
The analysis also revealed that different terminologies have been used by different syllabuses to describe the purpose of teaching mathematics at the secondary school level. Whereas Kenyan and Rwandan syllabuses use only two terms (general objectives and specific objectives), Tanzanian and Ugandan syllabuses use five different terms. In particular, the Tanzanian syllabus uses general competences, class competences, class objectives, general objectives, and specific objectives, while the Ugandan syllabus uses aims, competences, general objectives, specific objectives, and learning outcomes.
In some instances, there seems to be lack of clarity on how the different terms are being used in the syllabuses. For example, in the Ugandan O-level Mathematics syllabus, specific objectives are used to describe what the learners are to achieve by the end of a topic, in the Principal Mathematics syllabus, general objectives and specific objectives are used for topics and subtopics, respectively. In the Subsidiary Mathematics syllabus, meanwhile, learning outcomes and competencies are used for topics and subtopics, respectively. In the Rwandan A-level syllabus, general objectives are used to describe what the learners are to achieve by the end of A-level, by the end of a given year, and by the end of a given topic, while specific objectives are used to describe what the learners are to achieve by the end of a subtopic. In the O-level syllabus, there are no general objectives for topics, instead specific objectives are used to cater for both topics and subtopics.
In moving towards harmonization, it would be helpful to have clarity in the nomenclature used, so that the syllabus makes it clear what is expected of teachers and students and why. This issue is reconsidered in the conclusions. Furthermore, there is need to ensure that the aims and objectives of the mathematics curriculum keep pace with the competencies required in the regional labour market. For instance, ICT skills are very much needed in the current job market, and it would thus be good to have some of the aims and objectives reflect this reality.
Organizing Principles Embedded in the Mathematics Syllabuses
We compared the stated or implied philosophy of secondary mathematics teaching and learning in the four syllabuses, and observed that, generally, the underpinning philosophies in Kenya, Tanzania and Uganda reflect an emphasis on real-world applications of school mathematics. The Kenyan syllabus “has emphasized application of Mathematics to real life experiences and practical approaches to teaching and learning in an effort to address such contemporary issues as information technology, health, gender and integrity” (KIE 2002: 3). The Tanzanian syllabus emphasizes a paradigm shift from a content-based to a competency-based curriculum. The syllabus states that the teaching and learning processes should be student-centered and activity oriented (TIE 2005b: iii). The Ugandan O-level syllabus encourages “practical problem solving” and cooperative learning (NCDC–Uganda 2008: x), while the A-level syllabus emphasizes “effective and efficient acquisition of knowledge and development of concepts, skills, values and attitudes” (p. 119).
Meanwhile, the Rwandan syllabus appears to be content-oriented and prescriptive. In the general introduction, the key topics of the syllabus are listed. The O-level syllabus approaches each topic “in a systematic way while taking into account difficulties it presents and the learning age of the student who receives it” (NCDC–Rwanda 2006: 4), while the A-level syllabus has been prepared “in a format which helps teachers to teach a particular topic effectively” (NCDC–Rwanda 2010: 4). The syllabus underscores the need for an interdisciplinary approach to the teaching of mathematics; in other words, the need to “establish the relationship between Mathematics and other subjects” (p. 7).
In practice, it may be helpful to think of content and process not as antagonistic but, rather, as two sides of the same coin. As such, the match between the stated underpinning philosophy and what happens in the classroom would appear to be a very fruitful area for future research to pursue.
The Place of Mathematics in the Overall School Curriculum
In all the four countries, mathematics has a central and significant place in the school curriculum, as reflected in the number of hours allocated to mathematics (relative to the other subjects in the school curriculum) and the requirement for mathematics to be compulsory for some of the years of schooling.
The secondary education curriculum in Kenya emphasizes both compulsory and elective subjects. In the first and second years, students study 12 subjects whereas in the third and fourth years, they specialize and study between 5 and 9 subjects. Mathematics, English and Kiswahili are compulsory at all levels of secondary education. Performance of students in mathematics and English influences
their admission to various specialized programmes and courses in post-secondary institutions, thus determining their career path (Wasanga, Ogle, & Wambua 2012: 3). In Uganda (Karp, Opolot-Okurut, & Schubring 2014), Tanzania (TIE 2005a) and Rwanda (Republic of Rwanda 2013), mathematics is compulsory up to the end of ordinary secondary education. This means that, whilst Kenyan students have 12 years of compulsory mathematics education, their counterparts in Uganda and Tanzania have 11 years, while students in Rwanda have 9 years. In Tanzania, students who wish to study more mathematics at O-level can take “Additional Mathematics” in addition to the regular mathematics curriculum. The curriculum for additional mathematics is intended for the entire O-level cycle.
During the years of compulsory mathematics education, Kenya is the only country among the four under consideration that has two alternative routes for the secondary mathematics curriculum. Students joining secondary education can choose between ‘Mathematics Alternative A’ and ‘Mathematics Alternative B’ curriculum. The latter—a simpler version of Mathematics Alternative A curriculum— was developed in 2009 for students for whom secondary education is terminal or those whose career paths do not require intensive use of mathematics (KIE 2008). The mathematics curriculum is organized into topics and whereas Mathematics Alternative A curriculum has 68 topics, Mathematics Alternative B curriculum has 57 topics. The only new topic in Mathematics Alternative B curriculum is Cash Books, otherwise all the other topics are taken from Mathematics Alternative A curriculum. However, as noted in the next chapter, the uptake of Alternative B is extremely low, and it would appear in practice that there is still work to be done in ensuring a meaningful, challenging and enjoyable mathematics curriculum for all learners.
In Tanzania and Uganda, A-level students select a combination of three principal subjects to specialize in according to their interests and career goals. However, students who do not take mathematics as one of their principal subjects but have at least one principal subject that requires some mathematical background—for example, economics or physics—are required to take subsidiary mathematics. This subsidiary mathematics is not as rigorous as the one offered as a principal subject. Until 2014 in Tanzania ‘Basic Applied Mathematics’ was assessed just on a passfail basis, this continues to be the case with the equivalent in Uganda.
It is worth noting here that in Uganda, a project to reform the O-level curriculum is currently underway. According to the National Curriculum Development Centre (NCDC), the proposed curriculum seeks to shift from a strictly academic list of subjects to a set of generic skills that are to be acquired through eight compulsory learning areas; namely, Mathematics, Science, Languages, Social Studies, Creative Arts, Life Education, Religious Education, and Technology and Enterprise (NCDC-Uganda 2014). Currently, the O-level curriculum consists of 14 subjects, and the proposed curriculum framework seeks to merge and integrate these subjects. It is hoped that the new curriculum will provide learners with holistic education that will equip them with the requirements for the contemporary market. With respect to the mathematics learning area, the new curriculum will “move to the applicable and functional mathematics that is required by all learners
S. Karuku and G. Tennant
for full and effective participation in social and economic life” (p. 3). There will be a core programme of study for all learners and an extended programme designed specifically for high achievers and those going on to further studies in mathematics. A comparison of the current curriculum (NCDC-Uganda 2008) and the proposed curriculum (NCDC-Uganda 2014) would indicate that a number of topics are being dropped, including logarithms as a calculation aid, sets, matrices, functions and linear programming. Algebra is addressed with a noticeably more problem-solving approach. In the absence of any clearly stated timelines for the implementation of the new curriculum, it is the current curriculum which is subject to analysis in this chapter.
Analysis of the Subject Matter Content
Our analysis of the subject matter content in the syllabuses focused on five content strands in mathematics, namely, Number Sense and Operations, Algebra, Geometry, Probability and Statistics (Data Handling), and Measurement. In our analysis of each of these content strands, we were interested in the breadth (the content specified in each of the key ideas) and depth (the degree of emphasis given to the key ideas and the skills specified in relation to those ideas). We were also interested in the grade level at which specific content is introduced. Because of the continuum in mathematics from primary to secondary school, it was necessary to analyze the subject content in the pre-secondary school education as well. Based on this analysis, we identified the disparities and similarities between the syllabuses of the four countries. This section presents the results of the analysis of each of these four content strands.
It is worth noting that it is not always clear when one topic ends and another begins. For example, number sequences might be considered as either a Number Sense and Operations or an Algebra topic; similarly, quadratic equations can be considered both under the headings of Algebra and Geometry. In addition, there are instances where topics are explicitly mentioned in one country but not another, leaving a gap in the intended curriculum which may well be filled in practice. So, for example, place value is not explicitly mentioned in the Rwanda syllabus, and algebraic substitution is not explicitly mentioned in the Tanzanian syllabus. It is also important to reiterate that this was an analysis of the intended curriculum, not the taught curriculum, and still less the learnt curriculum.
Number Sense and Operations
There is a great level of commonality among the four syllabuses in terms of the breadth of coverage of the key concepts in Number Sense and Operations. However, there are differences in depth of coverage as well as in the grade level
at which some of these key concepts are introduced. Table 2.1 shows the year when some of the key skills in Number Sense and Operations are introduced in the mathematics syllabus.
It is noticeable particularly that different syllabuses have different emphases on approximation and estimation. For example, the Kenyan syllabus considers significant figures, absolute, relative, percentage, round-off, and truncation errors, propagation of errors from simple calculation, and maximum and minimum errors. The Ugandan syllabus, on the other hand, focuses on significant figures, decimal places, ‘rough’ answers, and sensible answers. The Tanzanian syllabus focuses on rounding off whole numbers to given place values; rounding off decimal numbers to a given number of decimal places, writing numbers to a given number of significant figures, and computations involving large and small numbers. For example, in Year 7, there is a discussion of the rounding-off of whole numbers to given place values or to a given number of significant figures. The Rwandan syllabus, meanwhile, has no explicit mention of this area of Number Sense.
It is noticeable that logarithms are still taught in Kenya, Tanzania and Uganda as a calculation aid, whereas in Rwanda they are introduced in the context of calculus. Furthermore, it is only in the Tanzanian mathematics curriculum that the use of ICT and calculators in mathematics is included in the curriculum; otherwise the other three countries do not make explicit mention of integration of ICT in mathematics.
Table 2.1 Year when various skills in number sense and operations are introduced Year when the skill is introduced Kenya Rwanda Tanzania Uganda
Place value 1 Not explicitly covered. There’s reference to ones, tens, hundreds, etc.
Number bases Not covered 5 8 (only base 10) 5
explicitly covered
Order of operations 9 (on fractions, integers, decimals)
Commutative, associative and distributive laws
Algebra
The following shows the introduction of algebra topics by Year across the region, without those topics in which the introduction was in the same Year in all countries (Table 2.2).
Table 2.2 Year when various skills in algebra are introduced
when the skill is introduced
Table 2.2 (continued)
Number systems with formal notation: integers, decimals, rationals
informally)
Note Years in brackets are those not compulsory in Rwanda
There are a large number of commonalities in the sequencing of algebra topics across the countries. For example, letters to represent numerical values is first introduced in Year 4 in Kenya and Rwanda and Year 5 in Uganda and Tanzania. There is similarly at most one year’s difference as to when simplification of algebraic expressions are introduced (5 or 6), solution of equations in one unknown (6), finding values of algebraic expressions through substitution (6 or 7), solving quadratic equations by factorization and completing the square (9 or 10), forming and solving linear inequalities (10 or 11) and linear programming, with two years’ discrepancy in solving simultaneous equations (Tanzania in Year 8, Rwanda and Kenya in Year 9, Uganda in Year 10).
One key difference is the positioning of number sequences. In Uganda and Rwanda this is in year 4, in Kenya and Uganda in year 10. Particularly in Uganda, there is the clear implication that number sequences are intended to be a means of starting to develop algebraic ideas then to formalize these ideas later. This is not so clear in Rwanda. However, in Kenya and Uganda number sequences are treated very formally from first introduction, consistent with the positioning at a later stage in the school curriculum.
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ANSWER to John Robinson of Leyden; ed. by Champlin Burrage. (Harvard
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ANTHONY, KATHARINE SUSAN. Margaret Fuller;
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Seventeen folk tales from as many countries compose this collection. Among them are: The food that belonged to all (America); The birds who befriended a king (Arabia); The cattle that came (Bulgaria); Lazy Taro (Japan); The prince and the eagle (Greece); The seven sheepfolds (Hungary); The clever companions (India); Tom of the goatskin (Ireland); Cap o ’ rushes (England); The little cabin boy (Norway); The chess players (Wales).
ARMSTRONG, DAVID MAITLAND.
Day before yesterday. il *$6 (5c) Scribner
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ASH, EDWIN LANCELOT. Problem of nervous breakdown. *$3.50 (4c) Macmillan 616.8
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ASHFORD, DAISY (MRS JAMES DEVLIN).
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“Quite a tome in quantity compared to ‘The young visiters’ but except in the most childish efforts, not so happily naïve in quality.”
Booklist 17:30 O ’20
“Nothing is to be found either in Sir James Barrie’s introduction to ‘The young visiters,’ or in Mr Cobb’s tribute to the author of these tales, to show us that they believe in the identity of Daisy Ashford or in the claim that their humor is a juvenile product. In fact, at times both seem to be writing in jest more than earnest, or with a superficial seriousness that scarcely attempts to cover up the jest. Sex is the basis of the humor in all these stories, as it was in ‘The young visiters.’”
E. F. E.
Boston Transcript p6 Jl 14 ’20 1150w
Cath World 111:836 S ’20 120w
Ind 103:54 Jl 10 ’20 160w
“None is in the same class with ‘The young visiters,’ though each has here and there a touch worthy of her best year, her tenth, her annus mirabilis.” Silas
New Repub 23:258 Jl 28 ’20 100w
N Y Times p14 Je 27 ’20 1850w
“We doubt whether the book will repeat the success of its predecessor. It is hard to say why one doesn’t get as much out of it, but probably it is because a little of this sort of thing is amusing while a good deal palls.”
Outlook 125:615 Ag 4 ’20 110w
“These five stories, with their deeply romantic titles, contain enough to give the admirers of the earlier book many of the same thrills of pleasure and amusement.”
Review 3:711 Jl 7 ’20 160w
“The present writer would unhesitatingly say that it is upon the subjects of meals and packing and costume that ‘Daisy Ashford’ shines pre-eminently.”
Spec 124:50 Jl 10 ’20 1100w
“‘A short story of love and marriage’ and ‘The jealous governes ’ have the truly original ring of the book that made Daisy Ashford’s name famous and her identity wondered at. But the longer efforts of the new volume are merely uninteresting stories amateurishly told. The charm of the precocious but still unsophisticated mind is gone. ”
Springf’d Republican p11a Ag 8 ’20 250w
“None of the surviving products of Miss Daisy Ashford’s pen is quite up to the standard of ‘The young visiters.’ The longest, ‘The hangman’s daughter,’ contains some amusing passages, but it is a more ambitious work, written at a later age, and gives the effect of a burlesque of a ‘ grown-up ’ s ’ novel more than of a spontaneous efflorescence of childhood.”
